The life expectancy of HIV-infected individuals has been dramatically improved with the introduction of combination antiretroviral therapy, but these drugs are unable to cure the infection due to the presence of latent virus that persists for decades in resting memory CD4+ T cells. If at any point treatment is stopped, this virus can reactivate and reseed the infection. Consequently, expensive and inconvenient therapy must be taken for life, and the risks of adverse effects, immunologic damage, and drug resistance are exacerbated. Major research efforts are now underway to develop therapies to cure the infection and allow individuals to safely stop antiretroviral drugs. These include methods to eliminate remaining viral reservoirs, using latency-reversing drugs or stem cell transplants, or to render infectable cells resistant to infection by gene-therapy. However, there are many challenges and unknowns about these proposed interventions. Patients must be followed for multiple years after stopping treatment to ensure that they are cured. The current assays to quantify the size of viral reservoirs and measures changes in response to therapy have very limited sensitivity. We lack short-term markers to predict eventual therapy success, or in vitro benchmarks to prioritize which drugs to move from the laboratory to the clinic. Two recent HIV-infected patients who received stem cell transplants had undetectable viral reservoirs and were thought to be cured, but rebounded after many months off treatment. New methods are needed to interpret these studies. I propose to develop mathematical and statistical tools to help predict and interpret the leading HIV eradication strategies under investigation. Specifically, this work will include 1) developing a mathematical framework to predict the reduction in the reservoir needed to discontinue treatment, and statistical tools to advise aspects of trial design such as sampling, follow-up and inferring drug efficacy; 2) probing reservoir dynamics during hematopoietic stem cell transplant and determining mechanisms of persistence; 3) modeling viral dynamics during administration of latency-reversing pharmacologic agents and developing methods to quantify their actions; 4) using models to elucidate design principles for gene therapy approaches to create HIV-resistance cells in vivo. This work will be carried out in close collaboration with physician-scientists who are actively testing these therapies. By providing tools and practical guidance that can be used to predict and interpret treatment outcomes, these methods can help accelerate the search for an HIV cure.